Ramsey Taxation Problem

Suppose there are two medical goods. Heart surgery and plastic (cosmetic) surgery. The market price for the heart surgery is $100k, the market price for plastic surgery is $10k. The price .com/economics/elasticity">elasticity of demand for heart surgery is -0.2. The price elasticity of demand for plastic surgery is -3.0. The government is considering a tax on the surgeries. The tax on heart surgery is denoted th, and the tax on plastic surgery is denoted tp.

a) Why did I choose to make the demand elasticity for plastic surgery large relative to heart surgery?

b) What is the equation for the optimal (Ramsey) value of th in terms of tp.

c) In a clearly written paragraph, comment on the relative size of th compared to tp, and why we are seeing this result.

d) Suppose the government has selected tax levels th and tp using the Ramsey rule. Furthermore, at those .com/economics/taxation">taxes, the market sells 300 thousand heart surgeries and 1.5 million plastic surgeries. Finally, the government collects $1 billion in revenue from these taxes. What are the values of th and tp?